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The Banach-Mazur Game

  • John C. Oxtoby
Part of the Graduate Texts in Mathematics book series (GTM, volume 2)

Abstract

Around 1928, the Polish mathematician S. Mazur invented the following mathematical “game.” Player (A) is “dealt” an arbitrary subset A of a closed interval I0. The complementary set B = I0A is dealt to player (B). The game 〈A, B〉 is played as follows: (A) chooses arbitrarily a closed interval I1I0; then (B) chooses a closed interval I2I1; then (A) chooses a closed interval I3I2; and so on, alternately. Together the players determine a nested sequence of closed intervals In, (A) choosing those with odd index, (B) those with even index. If the set ∩I n has at least one point in common with A, then (A) wins; otherwise, (B) wins.

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Copyright information

© Springer-Verlag New York 1971

Authors and Affiliations

  • John C. Oxtoby
    • 1
  1. 1.Bryn Mawr CollegeBryn MawrUSA

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